New statistical methods for analysis of the genetic component of complex familial diseases are needed in order to determine the relative contribution of environment and heredity to a variety of traits, and to elucidate the specifics of these determinants. We have been focussing on the problem of genetic linkage studies in complex diorders (e.g. arthritis, other autoimmune diseases, mitochondrial diseases) when certain usual conditions of analysis are not met (e.g. known mendelian model, large sample size, non-normally-distributed quantitative trait measurements).